The chemical reactivity of neutral, cationic, and anionic species of the gas phase B(13) cluster with molecular oxygen, O(2), was investigated using density functional theory. All three species of B(13) interact with an oxygen molecule to generate a variety of stable isomers, with those representing a dissociative chemisorption process forming the most stable configurations. Our results also show site-specific bonding of oxygen to the B(13)((+/0/-)) cluster. The effect of sequential ionization on the formation of products is pronounced. In ionic B(13) clusters, in addition to energetics, the spin of the reactants and products plays a vital role in determining the most favorable product channel. In addition, this study reveals a richness of phenomena requiring a unified consideration of energy, geometry, spin conversion, and details of the electronic structure not previously illustrated for the reactivity of boron clusters.